<p>Inspired by the increasing development of theories related to stability in the sense of Hyers–Ulam, Hyers–Ulam–Rassias, and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>–semi–Hyers–Ulam, this paper presents new sufficient conditions for establishing the stability of fuzzy fractional differential equations. This is achieved by employing fixed–point arguments in the framework of fuzzy–valued function spaces endowed with the Bielecki metric. After presenting the main theorems, illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results, followed by graphical simulations that visualize the behavior of the fuzzy solutions.</p>

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Ulam–type stability results for fractional differential equations with uncertainty

  • Natasha Irshad,
  • Rahim Shah,
  • Zubaria Waqar

摘要

Inspired by the increasing development of theories related to stability in the sense of Hyers–Ulam, Hyers–Ulam–Rassias, and \(\sigma \) σ –semi–Hyers–Ulam, this paper presents new sufficient conditions for establishing the stability of fuzzy fractional differential equations. This is achieved by employing fixed–point arguments in the framework of fuzzy–valued function spaces endowed with the Bielecki metric. After presenting the main theorems, illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results, followed by graphical simulations that visualize the behavior of the fuzzy solutions.